1. Field of the Invention
The invention relates to an N-dimensional filter having a transmission function for applying noise reduction to an original image pixel being provided to the N-dimensional filter by a received input-signal, wherein said transmission function comprises at least one filter-coefficient.
The invention further relates to a method for N-dimensionally filtering an original image pixel p according to a transmission function in order to apply noise reduction to said pixel p.
2. Description of the Related Art
Such N-dimensional filters or filtering methods are known in the art, e.g., from European Patent Application No. EP 0 682 841 B1, corresponding to U.S. Pat. Nos. 5,715,335 and 5,742,355, the contents of which is hereby incorporated by reference. In the European patent application, for every pixel position p=(x, y, t)T, where T indicates transposition, in an input luminance signal F(p), the filter transmission function Ff(p) is defined as follows:
                                          F            f                    ⁡                      (            p            )                          =                              G            ⁡                          (              p              )                                ·                      [                                                            F                  ⁡                                      (                    p                    )                                                  +                                  γ                  ⁢                                                            ∑                                              n                        ∈                                                  N                          1                                                                                      ⁢                                                                                  ⁢                                          α                      ⁡                                              (                                                  p                          ,                          n                                                )                                                                                                        ⁣              ⁣                                                ·                                      F                    ⁡                                          (                                              p                        +                        n                                            )                                                                      +                                  δ                  ⁢                                                            ∑                                              n                        ∈                                                  N                          2                                                                                      ⁢                                                                  β                        ⁡                                                  (                                                      p                            ,                            n                                                    )                                                                    ·                                                                        F                          f                                                ⁡                                                  (                                                      p                            +                            n                                                    )                                                                                                                                          ]                                              (        1        )            wherein    N1, N2: are sets of vectors defining one, two or three dimensional neighborhoods of one original image pixel;    n: identifies the position of an actual pixel within said neighborhoods N1, N2;    G(p): is a normalization factor;    α(p,n),: are filter coefficients of said N-dimensional filter, in particular, of said    β(p,n) transmission function Ff(p); and    γ, δ: are predefined constants.
Further, in said European patent application, the filter coefficients are defined as follows:
                              α          ⁡                      (                          p              ,              n                        )                          =                  {                                                                                        ⁢                                                            w1                      ⁢                                              :                                            ⁢                                                                                          ⁢                                              Δ                        ⁡                                                  (                                                      p                            ,                            n                                                    )                                                                                      <                                          Th                      1                                                                                                                                                                w2                    ⁢                                          :                                        ⁢                                                                                  ⁢                                          Th                      1                                                        ≤                                      Δ                    ⁡                                          (                                              p                        ,                        n                                            )                                                        >                                      Th                    2                                                                                                                                          ⁢                                                            0                      ⁢                                              :                                            ⁢                                                                                          ⁢                                              Δ                        ⁡                                                  (                                                      p                            ,                            n                                                    )                                                                                      ≥                                          Th                      2                                                                                                                              (        2        )                                          β          ⁡                      (                          p              ,              n                        )                          =                  {                                                                                        ⁢                                                            w1                      ⁢                                              :                                            ⁢                                                                                          ⁢                                                                        Δ                          f                                                ⁡                                                  (                                                      p                            ,                            n                                                    )                                                                                      <                                          Th                      1                                                                                                                                                                w2                    ⁢                                          :                                        ⁢                                                                                  ⁢                                          Th                      1                                                        ≤                                                            Δ                      f                                        ⁡                                          (                                              p                        ,                        n                                            )                                                        >                                      Th                    2                                                                                                                                          ⁢                                                            0                      ⁢                                              :                                            ⁢                                                                                          ⁢                                                                        Δ                          f                                                ⁡                                                  (                                                      p                            ,                            n                                                    )                                                                                      ≥                                          Th                      2                                                                                                                              (        3        )            wherein the parameters Δ and Δf are defined as follows:Δ(p,n)=|F(p+n)−F(p)|  (4)Δf(p,n)=|Ff(p+n)−F(p)|  (5)and whereinTh1, Th2: are predetermined threshold values; andw1, w2: are positive integer values.
FIG. 4 shows an example for a typical distribution of the magnitudes of the filter coefficients α(p, n) or β(p, n).
It is important to note that according to European Patent Application No. EP 0 682 841 B1, the filter coefficients α and β are defined such that the transmission function carries out only noise reduction to the input signal, i.e., in particular, to the original image pixel. In the case of the transmission function according to formula (1), this is achieved by defining the filter coefficients α and β always positive, as is done in formulas (2) and (3).
However, for improving the quality of images, very often noise reduction is not enough. Usually, also sharpness enhancement (peaking) of the image, and in particular, of the image pixels, is additionally required in receivers of an image signal. Traditionally these two operations have been implemented in series. In these cases, the noise filter has, for example, the transmission function (1) while the sharpness enhancement function is realized by another separated filter having quite another transmission function.
However, spectrally, this serial arrangement does not produce an optimal result. This is because noise reduction is commonly a low-pass-filtering operation, while peaking is a high-pass operation. Hence, there is a conflicting spectral demand on both filters and, generally, the optimization of one leads to deterioration of the other. If the noise reduction is done after the peaking, then the noise filter will remove the sharpness enhancement created by a peaking filter. Usually, the peaking is done after the noise filtering as this leads to a more acceptable behavior. However, this also requires some compromise since peaking tends to enhance remaining image noise.